Manifold Learning for Data-Driven Dynamical System Modeling

The goal of this project was to perform Proof of Concept (PoC) of a theory developed in the SIPL lab by Prof. Ronen Talmon and Or Yair. The theory describes an algorithm that is based on Manifold Learning tools, namely Diffusion Maps, and is used to analyze physical systems and their dynamics empirically – meaning without any prior knowledge.
The theory was previously only tested on simulated data, so our first and main objective was to perform the PoC by running the algorithm on data acquired from a real physical system. For simplicity, we chose the physical pendulum as our test system. We constructed such a pendulum and, using data acquired from smartphone sensors and a camera video, were able to determine the pendulum’s frequency empirically.
The project’s second objective was to design a real-time demo of the theory. Using Matlab’s AppDesigner, we created an application able to acquire a video and analyze it in real-time using the algorithm. The demo includes a graphical interface, and 3 physical systems: simple pendulum, elastic pendulum and coupled pendulum. It also includes live reconstruction of the system’s phase from the input video.
The demo was presented at IMVC 2019 in Tel Aviv, and at ICASSP 2019 in Brighton, England.